]> https://gitweb.dealii.org/ - dealii.git/commitdiff
AD: Add test for 4 component scalar function
authorJean-Paul Pelteret <jppelteret@gmail.com>
Mon, 22 Apr 2019 11:14:25 +0000 (13:14 +0200)
committerJean-Paul Pelteret <jppelteret@gmail.com>
Tue, 23 Apr 2019 15:50:18 +0000 (17:50 +0200)
13 files changed:
tests/ad_common_tests/helper_scalar_coupled_4_components_01.h [new file with mode: 0644]
tests/adolc/helper_scalar_coupled_4_components_01_1.cc [new file with mode: 0644]
tests/adolc/helper_scalar_coupled_4_components_01_1.output [new file with mode: 0644]
tests/adolc/helper_scalar_coupled_4_components_01_2.cc [new file with mode: 0644]
tests/adolc/helper_scalar_coupled_4_components_01_2.output [new file with mode: 0644]
tests/sacado/helper_scalar_coupled_4_components_01_1.cc [new file with mode: 0644]
tests/sacado/helper_scalar_coupled_4_components_01_1.output [new file with mode: 0644]
tests/sacado/helper_scalar_coupled_4_components_01_2.cc [new file with mode: 0644]
tests/sacado/helper_scalar_coupled_4_components_01_2.output [new file with mode: 0644]
tests/sacado/helper_scalar_coupled_4_components_01_3.cc [new file with mode: 0644]
tests/sacado/helper_scalar_coupled_4_components_01_3.output [new file with mode: 0644]
tests/sacado/helper_scalar_coupled_4_components_01_4.cc [new file with mode: 0644]
tests/sacado/helper_scalar_coupled_4_components_01_4.output [new file with mode: 0644]

diff --git a/tests/ad_common_tests/helper_scalar_coupled_4_components_01.h b/tests/ad_common_tests/helper_scalar_coupled_4_components_01.h
new file mode 100644 (file)
index 0000000..bf56e7d
--- /dev/null
@@ -0,0 +1,658 @@
+// ---------------------------------------------------------------------
+//
+// Copyright (C) 2019 by the deal.II authors
+//
+// This file is part of the deal.II library.
+//
+// The deal.II library is free software; you can use it, redistribute
+// it, and/or modify it under the terms of the GNU Lesser General
+// Public License as published by the Free Software Foundation; either
+// version 2.1 of the License, or (at your option) any later version.
+// The full text of the license can be found in the file LICENSE at
+// the top level of the deal.II distribution.
+//
+// ---------------------------------------------------------------------
+
+
+// Header file:
+// Evaluation of a coupled system
+//   (symmetric tensor + tensor + vector + scalar components)
+// using a helper class
+
+#include <deal.II/base/conditional_ostream.h>
+#include <deal.II/base/logstream.h>
+#include <deal.II/base/symmetric_tensor.h>
+#include <deal.II/base/tensor.h>
+
+#include <deal.II/differentiation/ad.h>
+
+#include <deal.II/fe/fe_values_extractors.h>
+
+#include <deal.II/lac/full_matrix.h>
+#include <deal.II/lac/vector.h>
+
+#include <iostream>
+
+#include "../tests.h"
+
+using namespace dealii;
+namespace AD = dealii::Differentiation::AD;
+
+// Function and its derivatives
+template <int dim, typename NumberType>
+struct FunctionsTestSymmetricTensorTensorVectorScalarCoupled
+{
+  static NumberType
+  det_t(const Tensor<2, dim, NumberType> &t)
+  {
+    return determinant(t);
+  }
+
+  static Tensor<2, dim, NumberType>
+  ddet_t_dt(const Tensor<2, dim, NumberType> &t)
+  {
+    return det_t(t) * transpose(invert(t));
+  }
+
+  static Tensor<4, dim, NumberType>
+  d2det_t_dt_dt(const Tensor<2, dim, NumberType> &t)
+  {
+    const Tensor<2, dim, NumberType> t_inv = invert(t);
+    Tensor<4, dim, NumberType>       dt_inv_trans_dt;
+    // https://en.wikiversity.org/wiki/Introduction_to_Elasticity/Tensors#Derivative_of_the_determinant_of_a_tensor
+    for (unsigned int i = 0; i < dim; ++i)
+      for (unsigned int j = 0; j < dim; ++j)
+        for (unsigned int k = 0; k < dim; ++k)
+          for (unsigned int l = 0; l < dim; ++l)
+            dt_inv_trans_dt[i][j][k][l] = -t_inv[l][i] * t_inv[j][k];
+
+    return det_t(t) * outer_product(transpose(t_inv), transpose(t_inv)) +
+           det_t(t) * dt_inv_trans_dt;
+  }
+
+  static NumberType
+  det_t(const SymmetricTensor<2, dim, NumberType> &t)
+  {
+    return determinant(t);
+  }
+
+  static SymmetricTensor<2, dim, NumberType>
+  ddet_t_dt(const SymmetricTensor<2, dim, NumberType> &t)
+  {
+    const SymmetricTensor<2, dim, NumberType> t_inv = invert(t);
+    return det_t(t) * t_inv;
+  }
+
+  static SymmetricTensor<4, dim, NumberType>
+  d2det_t_dt_dt(const SymmetricTensor<2, dim, NumberType> &t)
+  {
+    const SymmetricTensor<2, dim, NumberType> t_inv = invert(t);
+    SymmetricTensor<4, dim, NumberType>       dt_inv_dt;
+    // https://en.wikiversity.org/wiki/Introduction_to_Elasticity/Tensors#Derivative_of_the_determinant_of_a_tensor
+    for (unsigned int i = 0; i < dim; ++i)
+      for (unsigned int j = i; j < dim; ++j)
+        for (unsigned int k = 0; k < dim; ++k)
+          for (unsigned int l = k; l < dim; ++l)
+            dt_inv_dt[i][j][k][l] =
+              -0.5 * (t_inv[i][k] * t_inv[j][l] + t_inv[i][l] * t_inv[j][k]);
+
+    return det_t(t) * outer_product(t_inv, t_inv) + det_t(t) * dt_inv_dt;
+  }
+
+  static NumberType
+  v_squ(const Tensor<1, dim, NumberType> &v)
+  {
+    return v * v;
+  }
+
+  static Tensor<1, dim, NumberType>
+  dv_squ_dv(const Tensor<1, dim, NumberType> &v)
+  {
+    return 2.0 * v;
+  }
+
+  static Tensor<2, dim, NumberType>
+  d2v_squ_dv_dv(const Tensor<1, dim, NumberType> &v)
+  {
+    static const Tensor<2, dim, NumberType> I(
+      unit_symmetric_tensor<dim, NumberType>());
+    return 2.0 * I;
+  }
+
+  // --------------------------------------------------------------------------
+
+  // Here we define a pseudo-energy function that we wish to differentiate twice
+  // with respect to all variables
+
+  static const double sf;
+
+  static NumberType
+  psi(const SymmetricTensor<2, dim, NumberType> &st,
+      const Tensor<2, dim, NumberType> &         t,
+      const Tensor<1, dim, NumberType> &         v,
+      const NumberType &                         s)
+  {
+    return std::pow(det_t(st), 2) * std::pow(det_t(t), 2) *
+           std::pow(v_squ(v), 3) * std::pow(s, sf);
+  };
+
+  // --------------------------------------------------------------------------
+
+  // Here's the hand-calculated expansion of this energy functions first and
+  // second derivatives. Lots of fun...
+
+  static SymmetricTensor<2, dim, NumberType>
+  dpsi_dst(const SymmetricTensor<2, dim, NumberType> &st,
+           const Tensor<2, dim, NumberType> &         t,
+           const Tensor<1, dim, NumberType> &         v,
+           const NumberType &                         s)
+  {
+    return 2.0 * std::pow(det_t(st), 1) * ddet_t_dt(st) *
+           std::pow(det_t(t), 2) * std::pow(v_squ(v), 3) * std::pow(s, sf);
+  };
+
+  static Tensor<2, dim, NumberType>
+  dpsi_dt(const SymmetricTensor<2, dim, NumberType> &st,
+          const Tensor<2, dim, NumberType> &         t,
+          const Tensor<1, dim, NumberType> &         v,
+          const NumberType &                         s)
+  {
+    return 2.0 * std::pow(det_t(st), 2) * std::pow(det_t(t), 1) * ddet_t_dt(t) *
+           std::pow(v_squ(v), 3) * std::pow(s, sf);
+  };
+
+  static Tensor<1, dim, NumberType>
+  dpsi_dv(const SymmetricTensor<2, dim, NumberType> &st,
+          const Tensor<2, dim, NumberType> &         t,
+          const Tensor<1, dim, NumberType> &         v,
+          const NumberType &                         s)
+  {
+    return std::pow(det_t(st), 2) * std::pow(det_t(t), 2) * 3.0 *
+           std::pow(v_squ(v), 2) * dv_squ_dv(v) * std::pow(s, sf);
+  };
+
+  static NumberType
+  dpsi_ds(const SymmetricTensor<2, dim, NumberType> &st,
+          const Tensor<2, dim, NumberType> &         t,
+          const Tensor<1, dim, NumberType> &         v,
+          const NumberType &                         s)
+  {
+    return std::pow(det_t(st), 2) * std::pow(det_t(t), 2) *
+           std::pow(v_squ(v), 3) * sf * std::pow(s, sf - 1.0);
+  };
+
+  static SymmetricTensor<4, dim, NumberType>
+  d2psi_dst_x_dst(const SymmetricTensor<2, dim, NumberType> &st,
+                  const Tensor<2, dim, NumberType> &         t,
+                  const Tensor<1, dim, NumberType> &         v,
+                  const NumberType &                         s)
+  {
+    return 2.0 * std::pow(det_t(t), 2) * std::pow(v_squ(v), 3) *
+           (std::pow(det_t(st), 0) *
+              outer_product(ddet_t_dt(st), ddet_t_dt(st)) +
+            std::pow(det_t(st), 1) * d2det_t_dt_dt(st)) *
+           std::pow(s, sf);
+  };
+
+  static Tensor<4, dim, NumberType>
+  d2psi_dst_x_dt(const SymmetricTensor<2, dim, NumberType> &st,
+                 const Tensor<2, dim, NumberType> &         t,
+                 const Tensor<1, dim, NumberType> &         v,
+                 const NumberType &                         s)
+  {
+    return 4.0 * std::pow(det_t(st), 1) * std::pow(det_t(t), 1) *
+           outer_product(Tensor<2, dim, NumberType>(ddet_t_dt(st)),
+                         ddet_t_dt(t)) *
+           std::pow(v_squ(v), 3) * std::pow(s, sf);
+  };
+
+  static Tensor<3, dim, NumberType>
+  d2psi_dst_x_dv(const SymmetricTensor<2, dim, NumberType> &st,
+                 const Tensor<2, dim, NumberType> &         t,
+                 const Tensor<1, dim, NumberType> &         v,
+                 const NumberType &                         s)
+  {
+    return 2.0 * std::pow(det_t(t), 2) * std::pow(det_t(st), 1) * 3.0 *
+           std::pow(v_squ(v), 2) *
+           outer_product(Tensor<2, dim, NumberType>(ddet_t_dt(st)),
+                         dv_squ_dv(v)) *
+           std::pow(s, sf);
+  };
+
+  static SymmetricTensor<2, dim, NumberType>
+  d2psi_dst_x_ds(const SymmetricTensor<2, dim, NumberType> &st,
+                 const Tensor<2, dim, NumberType> &         t,
+                 const Tensor<1, dim, NumberType> &         v,
+                 const NumberType &                         s)
+  {
+    return 2.0 * std::pow(det_t(st), 1) * ddet_t_dt(st) *
+           std::pow(det_t(t), 2) * std::pow(v_squ(v), 3) * sf *
+           std::pow(s, sf - 1.0);
+  };
+
+  static Tensor<4, dim, NumberType>
+  d2psi_dt_x_dst(const SymmetricTensor<2, dim, NumberType> &st,
+                 const Tensor<2, dim, NumberType> &         t,
+                 const Tensor<1, dim, NumberType> &         v,
+                 const NumberType &                         s)
+  {
+    return 4.0 * std::pow(det_t(st), 1) * std::pow(det_t(t), 1) *
+           outer_product(ddet_t_dt(t),
+                         Tensor<2, dim, NumberType>(ddet_t_dt(st))) *
+           std::pow(v_squ(v), 3) * std::pow(s, sf);
+  };
+
+  static Tensor<4, dim, NumberType>
+  d2psi_dt_x_dt(const SymmetricTensor<2, dim, NumberType> &st,
+                const Tensor<2, dim, NumberType> &         t,
+                const Tensor<1, dim, NumberType> &         v,
+                const NumberType &                         s)
+  {
+    return 2.0 * std::pow(det_t(st), 2) * std::pow(v_squ(v), 3) *
+           (pow(det_t(t), 0) * outer_product(ddet_t_dt(t), ddet_t_dt(t)) +
+            std::pow(det_t(t), 1) * d2det_t_dt_dt(t)) *
+           std::pow(s, sf);
+  };
+
+  static Tensor<3, dim, NumberType>
+  d2psi_dt_x_dv(const SymmetricTensor<2, dim, NumberType> &st,
+                const Tensor<2, dim, NumberType> &         t,
+                const Tensor<1, dim, NumberType> &         v,
+                const NumberType &                         s)
+  {
+    return 2.0 * std::pow(det_t(st), 2) * std::pow(det_t(t), 1) * 3.0 *
+           std::pow(v_squ(v), 2) * outer_product(ddet_t_dt(t), dv_squ_dv(v)) *
+           std::pow(s, sf);
+  };
+
+  static Tensor<2, dim, NumberType>
+  d2psi_dt_x_ds(const SymmetricTensor<2, dim, NumberType> &st,
+                const Tensor<2, dim, NumberType> &         t,
+                const Tensor<1, dim, NumberType> &         v,
+                const NumberType &                         s)
+  {
+    return 2.0 * std::pow(det_t(st), 2) * std::pow(det_t(t), 1) * ddet_t_dt(t) *
+           std::pow(v_squ(v), 3) * sf * std::pow(s, sf - 1.0);
+  };
+
+  static Tensor<3, dim, NumberType>
+  d2psi_dv_x_dst(const SymmetricTensor<2, dim, NumberType> &st,
+                 const Tensor<2, dim, NumberType> &         t,
+                 const Tensor<1, dim, NumberType> &         v,
+                 const NumberType &                         s)
+  {
+    return 2.0 * std::pow(det_t(t), 2) * std::pow(det_t(st), 1) * 3.0 *
+           std::pow(v_squ(v), 2) *
+           outer_product(dv_squ_dv(v),
+                         Tensor<2, dim, NumberType>(ddet_t_dt(st))) *
+           std::pow(s, sf);
+  };
+
+  static Tensor<3, dim, NumberType>
+  d2psi_dv_x_dt(const SymmetricTensor<2, dim, NumberType> &st,
+                const Tensor<2, dim, NumberType> &         t,
+                const Tensor<1, dim, NumberType> &         v,
+                const NumberType &                         s)
+  {
+    return 2.0 * std::pow(det_t(st), 2) * std::pow(det_t(t), 1) * 3.0 *
+           std::pow(v_squ(v), 2) * outer_product(dv_squ_dv(v), ddet_t_dt(t)) *
+           std::pow(s, sf);
+  };
+
+  static Tensor<2, dim, NumberType>
+  d2psi_dv_x_dv(const SymmetricTensor<2, dim, NumberType> &st,
+                const Tensor<2, dim, NumberType> &         t,
+                const Tensor<1, dim, NumberType> &         v,
+                const NumberType &                         s)
+  {
+    return std::pow(det_t(st), 2) * std::pow(det_t(t), 2) * 3.0 *
+           (2.0 * std::pow(v_squ(v), 1) *
+              outer_product(dv_squ_dv(v), dv_squ_dv(v)) +
+            std::pow(v_squ(v), 2) * d2v_squ_dv_dv(v)) *
+           std::pow(s, sf);
+  };
+
+  static Tensor<1, dim, NumberType>
+  d2psi_dv_x_ds(const SymmetricTensor<2, dim, NumberType> &st,
+                const Tensor<2, dim, NumberType> &         t,
+                const Tensor<1, dim, NumberType> &         v,
+                const NumberType &                         s)
+  {
+    return std::pow(det_t(st), 2) * std::pow(det_t(t), 2) * 3.0 *
+           std::pow(v_squ(v), 2) * dv_squ_dv(v) * sf * std::pow(s, sf - 1.0);
+  };
+
+  static SymmetricTensor<2, dim, NumberType>
+  d2psi_ds_x_dst(const SymmetricTensor<2, dim, NumberType> &st,
+                 const Tensor<2, dim, NumberType> &         t,
+                 const Tensor<1, dim, NumberType> &         v,
+                 const NumberType &                         s)
+  {
+    return 2.0 * ddet_t_dt(st) * std::pow(det_t(t), 2) *
+           std::pow(det_t(st), 1) * std::pow(v_squ(v), 3) * sf *
+           std::pow(s, sf - 1.0);
+  };
+
+  static Tensor<2, dim, NumberType>
+  d2psi_ds_x_dt(const SymmetricTensor<2, dim, NumberType> &st,
+                const Tensor<2, dim, NumberType> &         t,
+                const Tensor<1, dim, NumberType> &         v,
+                const NumberType &                         s)
+  {
+    return 2.0 * std::pow(det_t(st), 2) * std::pow(det_t(t), 1) * ddet_t_dt(t) *
+           std::pow(v_squ(v), 3) * sf * std::pow(s, sf - 1.0);
+  };
+
+  static Tensor<1, dim, NumberType>
+  d2psi_ds_x_dv(const SymmetricTensor<2, dim, NumberType> &st,
+                const Tensor<2, dim, NumberType> &         t,
+                const Tensor<1, dim, NumberType> &         v,
+                const NumberType &                         s)
+  {
+    return std::pow(det_t(st), 2) * std::pow(det_t(t), 2) * 3.0 *
+           std::pow(v_squ(v), 2) * dv_squ_dv(v) * sf * std::pow(s, sf - 1.0);
+  };
+
+  static NumberType
+  d2psi_ds_x_ds(const SymmetricTensor<2, dim, NumberType> &st,
+                const Tensor<2, dim, NumberType> &         t,
+                const Tensor<1, dim, NumberType> &         v,
+                const NumberType &                         s)
+  {
+    return std::pow(det_t(st), 2) * std::pow(det_t(t), 2) *
+           std::pow(v_squ(v), 3) * sf * (sf - 1.0) * std::pow(s, sf - 2.0);
+  };
+};
+
+template <int dim, typename NumberType>
+const double
+  FunctionsTestSymmetricTensorTensorVectorScalarCoupled<dim, NumberType>::sf =
+    2.2;
+
+template <int dim, typename number_t, enum AD::NumberTypes ad_type_code>
+void
+test_symmetric_tensor_tensor_vector_scalar_coupled()
+{
+  using ADHelper         = AD::ScalarFunction<dim, ad_type_code, number_t>;
+  using ADNumberType     = typename ADHelper::ad_type;
+  using ScalarNumberType = typename ADHelper::scalar_type;
+
+  const unsigned int this_mpi_process =
+    Utilities::MPI::this_mpi_process(MPI_COMM_WORLD);
+  ConditionalOStream pcout(deallog.get_console(), this_mpi_process == 0);
+
+  pcout << "*** Test variables: Tensor + Vector + Scalar (coupled), "
+        << "dim = " << Utilities::to_string(dim) << ", "
+        << "Type code: " << static_cast<int>(ad_type_code) << std::endl;
+
+  // Values computed from the AD energy function
+  ScalarNumberType             psi;
+  Vector<ScalarNumberType>     Dpsi;
+  FullMatrix<ScalarNumberType> D2psi;
+
+  // Function and its derivatives
+  using func_ad =
+    FunctionsTestSymmetricTensorTensorVectorScalarCoupled<dim, ADNumberType>;
+
+  // Setup the variable components and choose a value at which to
+  // evaluate the tape
+  const FEValuesExtractors::SymmetricTensor<2> st_dof(0);
+  const FEValuesExtractors::Tensor<2>          t_dof(
+    SymmetricTensor<2, dim>::n_independent_components);
+  const FEValuesExtractors::Vector v_dof(
+    SymmetricTensor<2, dim>::n_independent_components +
+    Tensor<2, dim>::n_independent_components);
+  const FEValuesExtractors::Scalar s_dof(
+    SymmetricTensor<2, dim>::n_independent_components +
+    Tensor<2, dim>::n_independent_components +
+    Tensor<1, dim>::n_independent_components);
+  const unsigned int n_AD_components =
+    SymmetricTensor<2, dim>::n_independent_components +
+    Tensor<2, dim>::n_independent_components +
+    Tensor<1, dim>::n_independent_components + 1;
+  ADHelper ad_helper(n_AD_components);
+  ad_helper.set_tape_buffer_sizes(); // Increase the buffer size from the
+                                     // default values
+
+  SymmetricTensor<2, dim, ScalarNumberType> st =
+    unit_symmetric_tensor<dim, ScalarNumberType>();
+  for (unsigned int i = 0; i < st.n_independent_components; ++i)
+    st[st.unrolled_to_component_indices(i)] += 0.72 * (1.5 * i + 0.12);
+  Tensor<2, dim, ScalarNumberType> t =
+    unit_symmetric_tensor<dim, ScalarNumberType>();
+  for (unsigned int i = 0; i < t.n_independent_components; ++i)
+    t[t.unrolled_to_component_indices(i)] += 0.11 * (i + 0.125);
+  Tensor<1, dim, ScalarNumberType> v;
+  ScalarNumberType                 s = 0.57;
+  for (unsigned int i = 0; i < dim; ++i)
+    v[i] = 0.275 * (1.0 + i);
+
+  const int  tape_no = 1;
+  const bool is_recording =
+    ad_helper.start_recording_operations(tape_no /*material_id*/,
+                                         true /*overwrite_tape*/,
+                                         true /*keep*/);
+  if (is_recording == true)
+    {
+      ad_helper.register_independent_variable(st, st_dof);
+      ad_helper.register_independent_variable(t, t_dof);
+      ad_helper.register_independent_variable(v, v_dof);
+      ad_helper.register_independent_variable(s, s_dof);
+
+      const SymmetricTensor<2, dim, ADNumberType> st_ad =
+        ad_helper.get_sensitive_variables(st_dof);
+      const Tensor<2, dim, ADNumberType> t_ad =
+        ad_helper.get_sensitive_variables(t_dof);
+      const Tensor<1, dim, ADNumberType> v_ad =
+        ad_helper.get_sensitive_variables(v_dof);
+      ADNumberType s_ad = ad_helper.get_sensitive_variables(s_dof);
+
+      const ADNumberType psi(func_ad::psi(st_ad, t_ad, v_ad, s_ad));
+
+      ad_helper.register_dependent_variable(psi);
+      ad_helper.stop_recording_operations(false /*write_tapes_to_file*/);
+
+      pcout << "Recorded data..." << std::endl;
+      pcout << "independent variable values: " << std::flush;
+      if (this_mpi_process == 0)
+        ad_helper.print_values(pcout.get_stream());
+      pcout << "st_ad: " << st_ad << std::endl;
+      pcout << "t_ad: " << t_ad << std::endl;
+      pcout << "v_ad: " << v_ad << std::endl;
+      pcout << "s_ad: " << s_ad << std::endl;
+      pcout << "psi: " << psi << std::endl;
+      pcout << std::endl;
+    }
+  else
+    {
+      Assert(is_recording == true, ExcInternalError());
+    }
+
+  // Do some work :-)
+  // Set a new evaluation point
+  if (AD::ADNumberTraits<ADNumberType>::is_taped == true)
+    {
+      pcout << "Using tape with different values for independent variables..."
+            << std::endl;
+      ad_helper.activate_recorded_tape(tape_no);
+      st *= 0.48;
+      t *= 0.9;
+      v *= 0.63;
+      s *= 1.21;
+      ad_helper.set_independent_variable(st, st_dof);
+      ad_helper.set_independent_variable(t, t_dof);
+      ad_helper.set_independent_variable(v, v_dof);
+      ad_helper.set_independent_variable(s, s_dof);
+    }
+
+  pcout << "independent variable values: " << std::flush;
+  if (this_mpi_process == 0)
+    ad_helper.print_values(pcout.get_stream());
+
+  // Compute the function value, gradient and hessian for the new evaluation
+  // point
+  psi = ad_helper.compute_value();
+  ad_helper.compute_gradient(Dpsi);
+  if (AD::ADNumberTraits<ADNumberType>::n_supported_derivative_levels >= 2)
+    {
+      ad_helper.compute_hessian(D2psi);
+    }
+
+  // Output the full stored function, gradient vector and hessian matrix
+  pcout << "psi: " << psi << std::endl;
+  pcout << "Dpsi: \n";
+  if (this_mpi_process == 0)
+    Dpsi.print(pcout.get_stream());
+  if (AD::ADNumberTraits<ADNumberType>::n_supported_derivative_levels >= 2)
+    {
+      pcout << "D2psi: \n";
+      if (this_mpi_process == 0)
+        D2psi.print_formatted(pcout.get_stream(), 3, true, 0, "0.0");
+    }
+
+  // Extract components of the solution
+  const SymmetricTensor<2, dim, ScalarNumberType> dpsi_dst =
+    ad_helper.extract_gradient_component(Dpsi, st_dof);
+  const Tensor<2, dim, ScalarNumberType> dpsi_dt =
+    ad_helper.extract_gradient_component(Dpsi, t_dof);
+  const Tensor<1, dim, ScalarNumberType> dpsi_dv =
+    ad_helper.extract_gradient_component(Dpsi, v_dof);
+  const Tensor<0, dim, ScalarNumberType> dpsi_ds =
+    ad_helper.extract_gradient_component(Dpsi, s_dof);
+  pcout << "extracted Dpsi (st): " << dpsi_dst << "\n"
+        << "extracted Dpsi (t): " << dpsi_dt << "\n"
+        << "extracted Dpsi (v): " << dpsi_dv << "\n"
+        << "extracted Dpsi (s): " << dpsi_ds << "\n";
+
+  // Verify the result
+  using func =
+    FunctionsTestSymmetricTensorTensorVectorScalarCoupled<dim,
+                                                          ScalarNumberType>;
+  static const ScalarNumberType tol =
+    1e5 * std::numeric_limits<ScalarNumberType>::epsilon();
+  Assert(std::abs(psi - func::psi(st, t, v, s)) < tol,
+         ExcMessage("No match for function value."));
+  Assert(std::abs((dpsi_dst - func::dpsi_dst(st, t, v, s)).norm()) < tol,
+         ExcMessage("No match for first derivative."));
+  Assert(std::abs((dpsi_dt - func::dpsi_dt(st, t, v, s)).norm()) < tol,
+         ExcMessage("No match for first derivative."));
+  Assert(std::abs((dpsi_dv - func::dpsi_dv(st, t, v, s)).norm()) < tol,
+         ExcMessage("No match for first derivative."));
+  Assert(std::abs(dpsi_ds - func::dpsi_ds(st, t, v, s)) < tol,
+         ExcMessage("No match for first derivative."));
+
+  if (AD::ADNumberTraits<ADNumberType>::n_supported_derivative_levels >= 2)
+    {
+      const SymmetricTensor<4, dim, ScalarNumberType> d2psi_dst_x_dst =
+        ad_helper.extract_hessian_component(D2psi, st_dof, st_dof);
+      const Tensor<4, dim, ScalarNumberType> d2psi_dst_x_dt =
+        ad_helper.extract_hessian_component(D2psi, st_dof, t_dof);
+      const Tensor<3, dim, ScalarNumberType> d2psi_dst_x_dv =
+        ad_helper.extract_hessian_component(D2psi, st_dof, v_dof);
+      const Tensor<2, dim, ScalarNumberType> d2psi_dst_x_ds =
+        ad_helper.extract_hessian_component(D2psi, st_dof, s_dof);
+
+      const Tensor<4, dim, ScalarNumberType> d2psi_dt_x_dst =
+        ad_helper.extract_hessian_component(D2psi, t_dof, st_dof);
+      const Tensor<4, dim, ScalarNumberType> d2psi_dt_x_dt =
+        ad_helper.extract_hessian_component(D2psi, t_dof, t_dof);
+      const Tensor<3, dim, ScalarNumberType> d2psi_dt_x_dv =
+        ad_helper.extract_hessian_component(D2psi, t_dof, v_dof);
+      const Tensor<2, dim, ScalarNumberType> d2psi_dt_x_ds =
+        ad_helper.extract_hessian_component(D2psi, t_dof, s_dof);
+
+      const Tensor<3, dim, ScalarNumberType> d2psi_dv_x_dst =
+        ad_helper.extract_hessian_component(D2psi, v_dof, st_dof);
+      const Tensor<3, dim, ScalarNumberType> d2psi_dv_x_dt =
+        ad_helper.extract_hessian_component(D2psi, v_dof, t_dof);
+      const Tensor<2, dim, ScalarNumberType> d2psi_dv_x_dv =
+        ad_helper.extract_hessian_component(D2psi, v_dof, v_dof);
+      const Tensor<1, dim, ScalarNumberType> d2psi_dv_x_ds =
+        ad_helper.extract_hessian_component(D2psi, v_dof, s_dof);
+
+      const SymmetricTensor<2, dim, ScalarNumberType> d2psi_ds_x_dst =
+        ad_helper.extract_hessian_component(D2psi, s_dof, st_dof);
+      const Tensor<2, dim, ScalarNumberType> d2psi_ds_x_dt =
+        ad_helper.extract_hessian_component(D2psi, s_dof, t_dof);
+      const Tensor<1, dim, ScalarNumberType> d2psi_ds_x_dv =
+        ad_helper.extract_hessian_component(D2psi, s_dof, v_dof);
+      const Tensor<0, dim, ScalarNumberType> d2psi_ds_x_ds =
+        ad_helper.extract_hessian_component(D2psi, s_dof, s_dof);
+
+      pcout << "extracted Dpsi (t): " << dpsi_dt << "\n"
+            << "extracted Dpsi (v): " << dpsi_dv << "\n"
+            << "extracted Dpsi (s): " << dpsi_ds << "\n"
+            << "extracted D2psi (st,st): " << d2psi_dst_x_dst << "\n"
+            << "extracted D2psi (st,t): " << d2psi_dst_x_dt << "\n"
+            << "extracted D2psi (st,v): " << d2psi_dst_x_dv << "\n"
+            << "extracted D2psi (st,s): " << d2psi_dst_x_ds << "\n"
+            << "extracted D2psi (t,st): " << d2psi_dt_x_dst << "\n"
+            << "extracted D2psi (t,t): " << d2psi_dt_x_dt << "\n"
+            << "extracted D2psi (t,v): " << d2psi_dt_x_dv << "\n"
+            << "extracted D2psi (t,s): " << d2psi_dt_x_ds << "\n"
+            << "extracted D2psi (v,st): " << d2psi_dv_x_dst << "\n"
+            << "extracted D2psi (v,t): " << d2psi_dv_x_dt << "\n"
+            << "extracted D2psi (v,v): " << d2psi_dv_x_dv << "\n"
+            << "extracted D2psi (v,s): " << d2psi_dv_x_ds << "\n"
+            << "extracted D2psi (s,st): " << d2psi_ds_x_dst << "\n"
+            << "extracted D2psi (s,t): " << d2psi_ds_x_dt << "\n"
+            << "extracted D2psi (s,v): " << d2psi_ds_x_dv << "\n"
+            << "extracted D2psi (s,s): " << d2psi_ds_x_ds << "\n"
+            << std::endl;
+
+      Assert(std::abs(
+               (d2psi_dst_x_dst - func::d2psi_dst_x_dst(st, t, v, s)).norm()) <
+               tol,
+             ExcMessage("No match for second derivative."));
+      Assert(std::abs(
+               (d2psi_dst_x_dt - func::d2psi_dst_x_dt(st, t, v, s)).norm()) <
+               tol,
+             ExcMessage("No match for second derivative."));
+      Assert(std::abs(
+               (d2psi_dst_x_dv - func::d2psi_dst_x_dv(st, t, v, s)).norm()) <
+               tol,
+             ExcMessage("No match for second derivative."));
+      Assert(std::abs(
+               (d2psi_dst_x_ds - func::d2psi_dst_x_ds(st, t, v, s)).norm()) <
+               tol,
+             ExcMessage("No match for second derivative."));
+      Assert(std::abs(
+               (d2psi_dt_x_dst - func::d2psi_dt_x_dst(st, t, v, s)).norm()) <
+               tol,
+             ExcMessage("No match for second derivative."));
+      Assert(std::abs(
+               (d2psi_dt_x_dt - func::d2psi_dt_x_dt(st, t, v, s)).norm()) < tol,
+             ExcMessage("No match for second derivative."));
+      Assert(std::abs(
+               (d2psi_dt_x_dv - func::d2psi_dt_x_dv(st, t, v, s)).norm()) < tol,
+             ExcMessage("No match for second derivative."));
+      Assert(std::abs(
+               (d2psi_dt_x_ds - func::d2psi_dt_x_ds(st, t, v, s)).norm()) < tol,
+             ExcMessage("No match for second derivative."));
+      Assert(std::abs(
+               (d2psi_dv_x_dst - func::d2psi_dv_x_dst(st, t, v, s)).norm()) <
+               tol,
+             ExcMessage("No match for second derivative."));
+      Assert(std::abs(
+               (d2psi_dv_x_dt - func::d2psi_dv_x_dt(st, t, v, s)).norm()) < tol,
+             ExcMessage("No match for second derivative."));
+      Assert(std::abs(
+               (d2psi_dv_x_dv - func::d2psi_dv_x_dv(st, t, v, s)).norm()) < tol,
+             ExcMessage("No match for second derivative."));
+      Assert(std::abs(
+               (d2psi_dv_x_ds - func::d2psi_dv_x_ds(st, t, v, s)).norm()) < tol,
+             ExcMessage("No match for second derivative."));
+      Assert(std::abs(
+               (d2psi_ds_x_dst - func::d2psi_ds_x_dst(st, t, v, s)).norm()) <
+               tol,
+             ExcMessage("No match for second derivative."));
+      Assert(std::abs(
+               (d2psi_ds_x_dt - func::d2psi_ds_x_dt(st, t, v, s)).norm()) < tol,
+             ExcMessage("No match for second derivative."));
+      Assert(std::abs(
+               (d2psi_ds_x_dv - func::d2psi_ds_x_dv(st, t, v, s)).norm()) < tol,
+             ExcMessage("No match for second derivative."));
+      Assert(std::abs(d2psi_ds_x_ds - func::d2psi_ds_x_ds(st, t, v, s)) < tol,
+             ExcMessage("No match for second derivative."));
+    }
+}
diff --git a/tests/adolc/helper_scalar_coupled_4_components_01_1.cc b/tests/adolc/helper_scalar_coupled_4_components_01_1.cc
new file mode 100644 (file)
index 0000000..1c156e8
--- /dev/null
@@ -0,0 +1,47 @@
+// ---------------------------------------------------------------------
+//
+// Copyright (C) 2019 by the deal.II authors
+//
+// This file is part of the deal.II library.
+//
+// The deal.II library is free software; you can use it, redistribute
+// it, and/or modify it under the terms of the GNU Lesser General
+// Public License as published by the Free Software Foundation; either
+// version 2.1 of the License, or (at your option) any later version.
+// The full text of the license can be found in the file LICENSE at
+// the top level of the deal.II distribution.
+//
+// ---------------------------------------------------------------------
+
+
+// Evaluation of a coupled system
+//   (symmetric tensor + tensor + vector + scalar components)
+// using a helper class
+//
+// AD number type: ADOL-C taped
+
+#include "../ad_common_tests/helper_scalar_coupled_4_components_01.h"
+#include "../tests.h"
+
+int
+main(int argc, char **argv)
+{
+  Utilities::MPI::MPI_InitFinalize mpi_initialization(argc, argv, 1);
+  MPILogInitAll                    mpi_log;
+
+  deallog.push("Double");
+  {
+    test_symmetric_tensor_tensor_vector_scalar_coupled<
+      2,
+      double,
+      AD::NumberTypes::adolc_taped>();
+    test_symmetric_tensor_tensor_vector_scalar_coupled<
+      3,
+      double,
+      AD::NumberTypes::adolc_taped>();
+    deallog << "OK" << std::endl;
+  }
+  deallog.pop();
+
+  deallog << "OK" << std::endl;
+}
diff --git a/tests/adolc/helper_scalar_coupled_4_components_01_1.output b/tests/adolc/helper_scalar_coupled_4_components_01_1.output
new file mode 100644 (file)
index 0000000..aeccfbd
--- /dev/null
@@ -0,0 +1,3 @@
+
+DEAL:0:Double:OK
+DEAL:0:OK
diff --git a/tests/adolc/helper_scalar_coupled_4_components_01_2.cc b/tests/adolc/helper_scalar_coupled_4_components_01_2.cc
new file mode 100644 (file)
index 0000000..d21c08a
--- /dev/null
@@ -0,0 +1,47 @@
+// ---------------------------------------------------------------------
+//
+// Copyright (C) 2019 by the deal.II authors
+//
+// This file is part of the deal.II library.
+//
+// The deal.II library is free software; you can use it, redistribute
+// it, and/or modify it under the terms of the GNU Lesser General
+// Public License as published by the Free Software Foundation; either
+// version 2.1 of the License, or (at your option) any later version.
+// The full text of the license can be found in the file LICENSE at
+// the top level of the deal.II distribution.
+//
+// ---------------------------------------------------------------------
+
+
+// Evaluation of a coupled system
+//   (symmetric tensor + tensor + vector + scalar components)
+// using a helper class
+//
+// AD number type: ADOL-C tapeless
+
+#include "../ad_common_tests/helper_scalar_coupled_4_components_01.h"
+#include "../tests.h"
+
+int
+main(int argc, char **argv)
+{
+  Utilities::MPI::MPI_InitFinalize mpi_initialization(argc, argv, 1);
+  MPILogInitAll                    mpi_log;
+
+  deallog.push("Double");
+  {
+    test_symmetric_tensor_tensor_vector_scalar_coupled<
+      2,
+      double,
+      AD::NumberTypes::adolc_tapeless>();
+    test_symmetric_tensor_tensor_vector_scalar_coupled<
+      3,
+      double,
+      AD::NumberTypes::adolc_tapeless>();
+    deallog << "OK" << std::endl;
+  }
+  deallog.pop();
+
+  deallog << "OK" << std::endl;
+}
diff --git a/tests/adolc/helper_scalar_coupled_4_components_01_2.output b/tests/adolc/helper_scalar_coupled_4_components_01_2.output
new file mode 100644 (file)
index 0000000..aeccfbd
--- /dev/null
@@ -0,0 +1,3 @@
+
+DEAL:0:Double:OK
+DEAL:0:OK
diff --git a/tests/sacado/helper_scalar_coupled_4_components_01_1.cc b/tests/sacado/helper_scalar_coupled_4_components_01_1.cc
new file mode 100644 (file)
index 0000000..b7e2dd8
--- /dev/null
@@ -0,0 +1,61 @@
+// ---------------------------------------------------------------------
+//
+// Copyright (C) 2019 by the deal.II authors
+//
+// This file is part of the deal.II library.
+//
+// The deal.II library is free software; you can use it, redistribute
+// it, and/or modify it under the terms of the GNU Lesser General
+// Public License as published by the Free Software Foundation; either
+// version 2.1 of the License, or (at your option) any later version.
+// The full text of the license can be found in the file LICENSE at
+// the top level of the deal.II distribution.
+//
+// ---------------------------------------------------------------------
+
+
+// Evaluation of a coupled system
+//   (symmetric tensor + tensor + vector + scalar components)
+// using a helper class
+//
+// AD number type: Sacado DFad
+
+#include "../ad_common_tests/helper_scalar_coupled_4_components_01.h"
+#include "../tests.h"
+
+int
+main(int argc, char **argv)
+{
+  Utilities::MPI::MPI_InitFinalize mpi_initialization(argc, argv, 1);
+  MPILogInitAll                    mpi_log;
+
+  deallog.push("Double");
+  {
+    test_symmetric_tensor_tensor_vector_scalar_coupled<
+      2,
+      double,
+      AD::NumberTypes::sacado_dfad>();
+    test_symmetric_tensor_tensor_vector_scalar_coupled<
+      3,
+      double,
+      AD::NumberTypes::sacado_dfad>();
+    deallog << "OK" << std::endl;
+  }
+  deallog.pop();
+
+  deallog.push("Float");
+  {
+    // test_symmetric_tensor_tensor_vector_scalar_coupled<
+    //   2,
+    //   float,
+    //   AD::NumberTypes::sacado_dfad>();
+    // test_symmetric_tensor_tensor_vector_scalar_coupled<
+    //   3,
+    //   float,
+    //   AD::NumberTypes::sacado_dfad>();
+    deallog << "OK" << std::endl;
+  }
+  deallog.pop();
+
+  deallog << "OK" << std::endl;
+}
diff --git a/tests/sacado/helper_scalar_coupled_4_components_01_1.output b/tests/sacado/helper_scalar_coupled_4_components_01_1.output
new file mode 100644 (file)
index 0000000..80d2ce7
--- /dev/null
@@ -0,0 +1,4 @@
+
+DEAL:0:Double:OK
+DEAL:0:Float:OK
+DEAL:0:OK
diff --git a/tests/sacado/helper_scalar_coupled_4_components_01_2.cc b/tests/sacado/helper_scalar_coupled_4_components_01_2.cc
new file mode 100644 (file)
index 0000000..2a5ea8b
--- /dev/null
@@ -0,0 +1,61 @@
+// ---------------------------------------------------------------------
+//
+// Copyright (C) 2019 by the deal.II authors
+//
+// This file is part of the deal.II library.
+//
+// The deal.II library is free software; you can use it, redistribute
+// it, and/or modify it under the terms of the GNU Lesser General
+// Public License as published by the Free Software Foundation; either
+// version 2.1 of the License, or (at your option) any later version.
+// The full text of the license can be found in the file LICENSE at
+// the top level of the deal.II distribution.
+//
+// ---------------------------------------------------------------------
+
+
+// Evaluation of a coupled system
+//   (symmetric tensor + tensor + vector + scalar components)
+// using a helper class
+//
+// AD number type: Sacado DFad-DFad
+
+#include "../ad_common_tests/helper_scalar_coupled_4_components_01.h"
+#include "../tests.h"
+
+int
+main(int argc, char **argv)
+{
+  Utilities::MPI::MPI_InitFinalize mpi_initialization(argc, argv, 1);
+  MPILogInitAll                    mpi_log;
+
+  deallog.push("Double");
+  {
+    test_symmetric_tensor_tensor_vector_scalar_coupled<
+      2,
+      double,
+      AD::NumberTypes::sacado_dfad_dfad>();
+    test_symmetric_tensor_tensor_vector_scalar_coupled<
+      3,
+      double,
+      AD::NumberTypes::sacado_dfad_dfad>();
+    deallog << "OK" << std::endl;
+  }
+  deallog.pop();
+
+  deallog.push("Float");
+  {
+    // test_symmetric_tensor_tensor_vector_scalar_coupled<
+    //   2,
+    //   float,
+    //   AD::NumberTypes::sacado_dfad_dfad>();
+    // test_symmetric_tensor_tensor_vector_scalar_coupled<
+    //   3,
+    //   float,
+    //   AD::NumberTypes::sacado_dfad_dfad>();
+    deallog << "OK" << std::endl;
+  }
+  deallog.pop();
+
+  deallog << "OK" << std::endl;
+}
diff --git a/tests/sacado/helper_scalar_coupled_4_components_01_2.output b/tests/sacado/helper_scalar_coupled_4_components_01_2.output
new file mode 100644 (file)
index 0000000..80d2ce7
--- /dev/null
@@ -0,0 +1,4 @@
+
+DEAL:0:Double:OK
+DEAL:0:Float:OK
+DEAL:0:OK
diff --git a/tests/sacado/helper_scalar_coupled_4_components_01_3.cc b/tests/sacado/helper_scalar_coupled_4_components_01_3.cc
new file mode 100644 (file)
index 0000000..a46fd04
--- /dev/null
@@ -0,0 +1,61 @@
+// ---------------------------------------------------------------------
+//
+// Copyright (C) 2019 by the deal.II authors
+//
+// This file is part of the deal.II library.
+//
+// The deal.II library is free software; you can use it, redistribute
+// it, and/or modify it under the terms of the GNU Lesser General
+// Public License as published by the Free Software Foundation; either
+// version 2.1 of the License, or (at your option) any later version.
+// The full text of the license can be found in the file LICENSE at
+// the top level of the deal.II distribution.
+//
+// ---------------------------------------------------------------------
+
+
+// Evaluation of a coupled system
+//   (symmetric tensor + tensor + vector + scalar components)
+// using a helper class
+//
+// AD number type: Sacado Rad
+
+#include "../ad_common_tests/helper_scalar_coupled_4_components_01.h"
+#include "../tests.h"
+
+int
+main(int argc, char **argv)
+{
+  Utilities::MPI::MPI_InitFinalize mpi_initialization(argc, argv, 1);
+  MPILogInitAll                    mpi_log;
+
+  deallog.push("Double");
+  {
+    test_symmetric_tensor_tensor_vector_scalar_coupled<
+      2,
+      double,
+      AD::NumberTypes::sacado_rad>();
+    test_symmetric_tensor_tensor_vector_scalar_coupled<
+      3,
+      double,
+      AD::NumberTypes::sacado_rad>();
+    deallog << "OK" << std::endl;
+  }
+  deallog.pop();
+
+  deallog.push("Float");
+  {
+    // test_symmetric_tensor_tensor_vector_scalar_coupled<
+    //   2,
+    //   float,
+    //   AD::NumberTypes::sacado_rad>();
+    // test_symmetric_tensor_tensor_vector_scalar_coupled<
+    //   3,
+    //   float,
+    //   AD::NumberTypes::sacado_rad>();
+    deallog << "OK" << std::endl;
+  }
+  deallog.pop();
+
+  deallog << "OK" << std::endl;
+}
diff --git a/tests/sacado/helper_scalar_coupled_4_components_01_3.output b/tests/sacado/helper_scalar_coupled_4_components_01_3.output
new file mode 100644 (file)
index 0000000..80d2ce7
--- /dev/null
@@ -0,0 +1,4 @@
+
+DEAL:0:Double:OK
+DEAL:0:Float:OK
+DEAL:0:OK
diff --git a/tests/sacado/helper_scalar_coupled_4_components_01_4.cc b/tests/sacado/helper_scalar_coupled_4_components_01_4.cc
new file mode 100644 (file)
index 0000000..22b9bbe
--- /dev/null
@@ -0,0 +1,61 @@
+// ---------------------------------------------------------------------
+//
+// Copyright (C) 2019 by the deal.II authors
+//
+// This file is part of the deal.II library.
+//
+// The deal.II library is free software; you can use it, redistribute
+// it, and/or modify it under the terms of the GNU Lesser General
+// Public License as published by the Free Software Foundation; either
+// version 2.1 of the License, or (at your option) any later version.
+// The full text of the license can be found in the file LICENSE at
+// the top level of the deal.II distribution.
+//
+// ---------------------------------------------------------------------
+
+
+// Evaluation of a coupled system
+//   (symmetric tensor + tensor + vector + scalar components)
+// using a helper class
+//
+// AD number type: Sacado Rad-DFad
+
+#include "../ad_common_tests/helper_scalar_coupled_4_components_01.h"
+#include "../tests.h"
+
+int
+main(int argc, char **argv)
+{
+  Utilities::MPI::MPI_InitFinalize mpi_initialization(argc, argv, 1);
+  MPILogInitAll                    mpi_log;
+
+  deallog.push("Double");
+  {
+    test_symmetric_tensor_tensor_vector_scalar_coupled<
+      2,
+      double,
+      AD::NumberTypes::sacado_rad_dfad>();
+    test_symmetric_tensor_tensor_vector_scalar_coupled<
+      3,
+      double,
+      AD::NumberTypes::sacado_rad_dfad>();
+    deallog << "OK" << std::endl;
+  }
+  deallog.pop();
+
+  deallog.push("Float");
+  {
+    // test_symmetric_tensor_tensor_vector_scalar_coupled<
+    //   2,
+    //   float,
+    //   AD::NumberTypes::sacado_rad_dfad>();
+    // test_symmetric_tensor_tensor_vector_scalar_coupled<
+    //   3,
+    //   float,
+    //   AD::NumberTypes::sacado_rad_dfad>();
+    deallog << "OK" << std::endl;
+  }
+  deallog.pop();
+
+  deallog << "OK" << std::endl;
+}
diff --git a/tests/sacado/helper_scalar_coupled_4_components_01_4.output b/tests/sacado/helper_scalar_coupled_4_components_01_4.output
new file mode 100644 (file)
index 0000000..80d2ce7
--- /dev/null
@@ -0,0 +1,4 @@
+
+DEAL:0:Double:OK
+DEAL:0:Float:OK
+DEAL:0:OK

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